Probability with independent outcomes

In summary, the conversation discusses the probability of a family having three children, all of whom are girls. The conversation includes different calculations and equations, and there is a discrepancy between the answer given in the book (0.115) and the calculated probability (0.125). The conversation also briefly mentions another question about the probability of the eldest child being a boy and the two youngest being girls, with a similar discrepancy in the given answer.
  • #1
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Jeeserssweesers(for a lack of a better word), probability is confusing.

Homework Statement



A family has three children, no twins or.. that same just with three.
a| What is the chance that all the children are girls.

Homework Equations



The chapter here shows the equtations P(a)+P(b)=P(a)xP(b), but my problem here maybe is that I don't find the use of that in this question.

The Attempt at a Solution



This questions looks just like the same to me when you throw three coins and ask what the chance is for that you get three on one side(?). So I get 2(boy or girl)x2x2= 8 possible outcomes. And getting three on one side is one out of these 8 outcomes, same with getting three girls. So that gives: 1/8. (=0.125). But in my book the result shows 0.115.
 
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  • #2
Yes, there are 8 possible outcomes: BBB, BBG, BGB, GBB, BGG, GBG, GGB, and GGG. 1 out of those 8 is GGG so the probability of "all girls" is 1/8= 0.125 as you say. I suspect that "0.115" is a typo.
 
  • #3
Yeah, I guessed so too, but then I've thought so before too and being wrong, so.. *g* Hm, I'll ask about b| soon.
 
  • #4
Yeah, b| the probability of that the eldest is a brother, and the two youngest girls. That is also just one outcomes yes? So that should give 1/8. But the answer writes as 0.121, which is not 1/8. ?
 
  • #5
Yes, that would be specifically "GGB" and the probability is (1/2)(1/2)(1/2)= 1/8= 0.125. Surely they don't have another typo? This is beginning to look like shoddy editing!
 
  • #6
uh, are you joking with me, or am I writing down the question wrong(cause I know I have a bad habit of not reading the question at probability well enough)? Cause that was the way I was thinking as you above.
 

What is the definition of probability with independent outcomes?

Probability with independent outcomes refers to the likelihood of a particular event occurring when the outcome of that event is not influenced by any other events or factors. In other words, the outcome of one event does not affect the outcome of another event.

How is the probability of independent outcomes calculated?

The probability of independent outcomes is calculated by multiplying the individual probabilities of each event. For example, if the probability of event A is 0.5 and the probability of event B is 0.3, then the probability of both events occurring is 0.5 x 0.3 = 0.15.

What is the relationship between independent outcomes and dependent outcomes?

Independent outcomes and dependent outcomes are two types of events in probability. Independent outcomes refer to events that are not influenced by each other, while dependent outcomes refer to events that are influenced by each other. This means that the outcome of one event affects the outcome of another event in dependent outcomes, but not in independent outcomes.

How can you identify independent outcomes in a probability problem?

To identify independent outcomes in a probability problem, you should look for events that do not affect each other. This can be determined by asking if the outcome of one event affects the likelihood of the other event occurring. If the answer is no, then the events are independent.

What are some real-life examples of independent outcomes?

Some real-life examples of independent outcomes include flipping a coin multiple times, rolling a die, and drawing cards from a deck without replacing them. In each of these situations, the outcome of one event does not affect the outcome of the other events.

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